olga has a drawer of socks with 4 red pairs, 2 gray pairs, and 8 black pairs. she also has a bag of…

olga has a drawer of socks with 4 red pairs, 2 gray pairs, and 8 black pairs. she also has a bag of hairbands with 10 red, 6 gray, and 24 black hairbands.\nif she selects randomly, what is the probability that olga will select a red pair of socks and a red hairband?\nclick the arrows to choose an answer from each menu.\nthe probability that olga will randomly select a red pair of socks is choose... , and the probability that she will randomly select a red hairband is choose... . the probability that she will select a red pair of socks and a red hairband is choose... .

olga has a drawer of socks with 4 red pairs, 2 gray pairs, and 8 black pairs. she also has a bag of hairbands with 10 red, 6 gray, and 24 black hairbands.\nif she selects randomly, what is the probability that olga will select a red pair of socks and a red hairband?\nclick the arrows to choose an answer from each menu.\nthe probability that olga will randomly select a red pair of socks is choose... , and the probability that she will randomly select a red hairband is choose... . the probability that she will select a red pair of socks and a red hairband is choose... .

Answer

Answer:

The probability that Olga will randomly select a red pair of socks is $\frac{4}{4 + 2+8}=\frac{4}{14}=\frac{2}{7}$, and the probability that she will randomly select a red hair - band is $\frac{10}{10 + 6+24}=\frac{10}{40}=\frac{1}{4}$. The probability that she will select a red pair of socks and a red hair - band is $\frac{2}{7}\times\frac{1}{4}=\frac{1}{14}$.

Explanation:

Step1: Calculate sock probability

Find total sock pairs: $4 + 2+8 = 14$. Red sock pairs are 4. So red sock probability is $\frac{4}{14}=\frac{2}{7}$.

Step2: Calculate hair - band probability

Find total hair - bands: $10 + 6+24 = 40$. Red hair - bands are 10. So red hair - band probability is $\frac{10}{40}=\frac{1}{4}$.

Step3: Calculate combined probability

Use multiplication rule for independent events. $\frac{2}{7}\times\frac{1}{4}=\frac{1}{14}$.